Percentage Calculator

Almost every percentage question people actually ask is one of three problems, and this calculator solves all three at once from two numbers. What is X% of Y — the discount, the tip, the tax. X is what percent of Y — the score, the share, the proportion. And what is the percentage change from X to Y — the raise, the price increase, the growth rate. They look like different questions but they are the same relationship rearranged, and the reason people find percentages awkward is usually that they are trying to recall three separate procedures instead of one. Enter your two numbers and read whichever line matches your question. The sections below cover the traps: why a 50% loss needs a 100% gain to recover, and why percentage points and percent are not the same thing.

How this is calculated

X% of Y = (X ÷ 100) × Y. X as a percentage of Y = (X ÷ Y) × 100. Percentage change from X to Y = ((Y − X) ÷ X) × 100.

Worked example with X = 25 and Y = 80: 25% of 80 is 20. 25 is 31.25% of 80. And the change from 25 to 80 is ((80 − 25) ÷ 25) × 100 = 220%.

The critical detail in the third formula is that you divide by the original value, not the new one. Dividing by the wrong number is the single most common percentage error, and it produces a result that is plausible enough to go unnoticed.

Why a 50% loss needs a 100% gain to recover

Percentage changes are not symmetric, because each one is measured against a different base. Losing 50% of 100 leaves 50. Gaining 50% of 50 gives 75, not 100 — you need to gain 100% of the reduced amount to get back.

The general rule: to recover from a loss of L percent, you need a gain of L ÷ (100 − L) × 100 percent. A 20% loss needs a 25% gain. A 75% loss needs a 300% gain. This asymmetry is why avoiding large drawdowns matters disproportionately in investing, and why 'down 40%, then up 40%' leaves you 16% below where you started.

Percentage points are not percent

If an interest rate rises from 4% to 5%, that is an increase of one percentage point, or an increase of 25 percent. Both are correct descriptions of the same change, and they differ by a factor of 25.

The distinction matters wherever the quantity being measured is itself a percentage — interest rates, tax rates, unemployment, market share, conversion rates. A headline saying a rate 'rose 25%' when it moved from 4% to 5% is technically true and routinely misread as a move to 29%. When you see a percentage change applied to a percentage, check which is meant.

How to use the percentage calculator

Enter your two numbers. Order matters for the change calculation — the first is the original, the second the new value.
Read the line that matches your question. All three results are shown at once, so pick the one whose phrasing matches what you asked.
Check the base for a change calculation. Percentage change always divides by the original value. If the answer looks too small, you may have the two numbers the wrong way round.

Frequently asked questions

How do I calculate percentage increase?

Percentage change = (new − old) ÷ old × 100. Going from 200 to 250 is (250−200)/200 × 100 = 25% increase.

What is the difference between percent and percentage points?

If a rate goes from 4% to 5%, that is one percentage point, or 25 percent. Both describe the same change and they differ by a factor of 25. The distinction matters whenever the thing changing is itself a percentage — interest rates, tax rates, conversion rates.

How do I work out what percentage one number is of another?

Divide the part by the whole and multiply by 100. 25 out of 80 is (25 ÷ 80) × 100 = 31.25%. The most common mistake is dividing the wrong way round, which gives 320% and should be an obvious signal that the two numbers were swapped.

Is a 50% loss undone by a 50% gain?

No. After −50%, you need +100% to get back to the start, because the gain applies to the smaller base.